1307 



6.. 



O 



O 



«'.. + £^-/J' 



•t* a. 



3/1 «O' 



«'s4 = "34 f 2/1 «»i + y,«„. 



^''44 =«44 + .Vl «4, 4 ^,«41' 



(34) 



where 



^11 =«11 — •'^1 «SI — yi «4P 



^1 " «Ql — -^«81 — y, «41' 

 «'s» = «SS + '^"l «ai -f '^3 «8S' 

 «'4s =«48 + -^1 «4. + ■'■a«4ï' 



and the miillipliers x^, .i\, ?/,, ?/, are determined by 



«II + '^'i «n + .^•, «1, — .t-, (a',, + 7^'") — y, a\,=0 

 «s« f '^'i «,i + -^i «,, - -^ï («'„ 4- ^') — .V, «'4, = O 

 «14 + .Vl «11 + y, «1, — ?/i (a'44 + ^') — -^'i «'t4 = O 



«,4 + yi «ai -f y» «5j — .V» («'44 + E') — '^ «'s4 = ^ 



The determinant is tlius reduced to the product of two determinants. 

 In our case we will in this way "peel off" 16 rows and columns 

 at a time, instead of two. It follows from (34) that a-,- and y; are 

 of the second order at least. The corrections 



bij — aij 



to be applied to the inner terms are thus of the fourth oider. If 

 now we proceed to remove the columns and rows of another 

 argument F, the effect of these corrections on the central determinant 

 will be of the sixth order. Consequently, if we agree to neglect 

 quantities of the sixth order in [i*, and therefore, since /? itself is 

 of the first order, quantities of the fifth order (i.e. of the order of 

 10—10) in ^^ (hen the rows and columns of each argument can be 

 removed separately, independently of all other arguments. The 

 determinant finally is reduced to a product of an infinite number 

 of determinants, of which the central one has 8 columns and rows, 

 and all others 16. Each of these corresponds I0 one argument =b E. 

 As has been pointed out above, to each root ^^ belongs a root 

 ^q -\- E and a root ^^ — E. It is thus evidently only necessary to 

 determine the 8 roots of the corrected central determinant. The 

 corrections which have been applied to the elements of the central 

 square are at least of the fourth order. These 8 lOOts will therefore 

 differ very little from those of the uncorrected determinant A, of 

 which three are zero. For the corrected determinant the relations 

 (29) do not hold, and also the a priori reasoning by which we 



